Tilden won the popular vote over Hayes in 1876. But the electoral college was hijacked by the Republican Party and a Congressional committee awarded the presidency to Hayes.
Benjamin Harrison won the electoral college in 1888 but lost the popular vote to the incumbent Cleveland. Cleveland returned the favor by unseating the incumbent Harrison four years later.
No one won the electoral college in 1824. Andrew Jackson won the popular vote and led the electoral college with an insufficient number to claim victory. Third place candidate Henry Clay threw his support to John Quincy Adams and they over-rode Jackson the in the House of Representatives. When Adams promptly named Clay his Secretary of State (traditional grooming post for the presidency then) Jackson's supporters had a fit. Adams spent four useless years as a lame duck president and Jackson trounced him at the polls in 1828.

Jesus Fucking Christ, seriously OP? You actually had to ask this question? Seriously? You couldn't just go look it up yourself?

How old are you, OP?

Girl, it's possible. Let's say every state that gave electoral votes to the loser was mostly a landslide in the loser's favor (ex: 90 % to 10 %). Now let's say every state that voted for the winner was like 51% to 49 %. So the winner would win the required amount of electoral votes, but the popular vote would go to the loser. Make sense? Happened with Bush.